nLab EV operads

(under construction)

Idea

If $V$ is a real orthogonal $G$-representation, then the topological little disks operad $D_{|V|}$ has a $G \times \Sigma_n$ action on its $n$-ary space, so it presents an object in the graph model structure on G-operads; under Bonventre‘s genuine operadic nerve, this presents a G-∞-operad called $\mathbb{E}_V$.

Properties

$G$-symmetric monoidal envelope

G-symmetric monoidal envelope

(…)

Related concepts

• Parametrized Higher Category Theory and Higher Algebra

• equivariant symmetric monoidal category, G-∞-operad

• indexing system

• algebraic pattern

References

As a graph $G$-operad,

• Bertrand Guillou, J. P. May?: Equivariant iterated loop space theory and permutative G-categories (2012) (arXiv:1207.3459)

On the genuine operadic nerve:

• Peter Bonventre?: The genuine operadic nerve (2019) (arXiv:1904.01465)

• Asaf Horev?: Genuine equivariant factorization homology (2019) (arXiv:1910.07226)